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D RAFT VERSION O CTOBER 10, 2013
Preprint typeset using LATEX style emulateapj v. 7/15/03
A SUPER-JUPITER ORBITING A LATE-TYPE STAR: A REFINED ANALYSIS OF MICROLENSING EVENT
OGLE-2012-BLG-0406.
Y. T SAPRAS1,R1,♠ , J.-Y. C HOIK1 , R. A. S TREET 1,♠, C. H ANK1,⋆,‡ , V. B OZZAN3,♦ , A. G OULDU 1,‡ , M. D OMINIK∗R3,♦,♠,♣ , J.-P.
B EAULIEUP4,♣ , A. U DALSKIO1, , U. G. J ØRGENSENN1,♦ , T. S UMIM1,† ,
arXiv:1310.2428v1 [astro-ph.EP] 9 Oct 2013
AND
D. M. B RAMICHR2,R6 , P. B ROWNE R3,♦ , K. H ORNE R3,♣ , M. H UNDERTMARKR3,♦ , S. I PATOVN2 , N. K AINSR2,♦ , C. S NODGRASSR5,♦ , I. A.
S TEELE R4,
(T HE ROBO N ET C OLLABORATION ),
K. A. A LSUBAIN2 , J. M. A NDERSENN9 , S. C ALCHI N OVATIN3,N18 , Y. DAMERDJIN8 , C. D IEHL N15,N17 , A. E LYIVN8,N19 , E. G IANNININ15 , S.
H ARDISN1 , K. H ARPSØE N5 , T. C. H INSE N1,N10,N11 , D. J UNCHERN1 , E. K ERINSN12 , H. KORHONENN1 , C. L IEBIGR3 , L. M ANCININ13 , M.
M ATHIASENN1 , M. T. P ENNYU 1 , M. R ABUSN14 , S. R AHVARN6 , G. S CARPETTAN3,N4,N16, J. S KOTTFELT N1,N5, J. S OUTHWORTHN7 , J.
S URDEJN8 , J. T REGLOAN -R EEDN7, C. V ILELAN7 , J. WAMBSGANSSN15
(T HE M I NDSTE P C OLLABORATION ),
S. KOZŁOWSKIO1 , M. K UBIAKO1 , P. P IETRUKOWICZ O1, G. P IETRZY ŃSKIO1,O2, R. P OLESKIO1,U 1, J. S KOWRONO1 , I. S OSZY ŃSKIO1 , M. K.
S ZYMA ŃSKIO1 , K. U LACZYKO1 , Ł UKASZ W YRZYKOWSKIO1,O3
(T HE OGLE C OLLABORATION ),
M. D. A LBROWP1 , E. BACHELET P2,P3, R. BARRYP11 , V. BATISTAP4 , A. B HATTACHARYAM10, S. B RILLANT P5, J. A. R. C ALDWELL P6 , A.
C ASSANP4 , A. C OLE P7 , E. C ORRALESP4 , C H . C OUTURESP4 , S. D IETERSP2 , D. D OMINIS P RESTERP8 , J. D ONATOWICZ P9 , P.
F OUQUÉ P2,P3 , J. G REENHILL P7, S. R. K ANE P10 , D. K UBASP4,P5 , J.-B. M ARQUETTE P4 , J. M ENZIESP12 , K. R. P OLLARDP1 , D. W OUTERSP4
(T HE PLANET C OLLABORATION ),
G. C HRISTIEU 6, D. L. D E P OYU 2 , S. D ONGU 3 , J. D RUMMONDU 9 , B. S. G AUDIU 1 , C. B. H ENDERSONU 1, K. H. H WANGK1 , Y. K. J UNGK1 ,
A. K AVKAU 1 , J.-R. KOOU 4 , C.-U. L EEU 4 , D. M AOZU 10 , L. A. G. M ONARDU 5 , T. NATUSCHU 6 , H. N GANU 6 , H. PARKK1 , R. W. P OGGEU 1 ,
I. P ORRITTU 7, I.-G. S HINK1 , Y. S HVARTZVALDU 10, T. G. TANU 8 , J. C. Y EEU 1
(T HE µFUN C OLLABORATION ),
F. A BE M2 , D. P. B ENNETT M10 , I. A. B ONDM3 , C. S. B OTZLERM4, M. F REEMANM4 , A. F UKUIM6 , D. F UKUNAGAM2 , Y. I TOWM2 , N.
KOSHIMOTOM1 , C. H. L INGM3 , K. M ASUDAM2 , Y. M ATSUBARAM2 , Y. M URAKIM2 , S. NAMBAM1 , K. O HNISHIM7 , N. J. R ATTENBURYM4 ,
T O . S AITOM8 , D. J. S ULLIVANM5 , W. L. S WEATMANM3 , D. S UZUKIM1 , P. J. T RISTRAMM9 , N. T SURUMIM2 , K. WADAM1 , N. YAMAIM11 ,
P. C. M. YOCKM4 A. YONEHARAM11
(T HE MOA C OLLABORATION )
1 Las
Cumbres Observatory Global Telescope Network, 6740 Cortona Drive, suite 102, Goleta, CA 93117, USA
K1 Department of Physics, Chungbuk National University, Cheongju 361-763, Republic of Korea
R1 School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, UK
R2 European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching bei München, Germany
R3 SUPA, School of Physics & Astronomy, University of St Andrews, North Haugh, St Andrews KY16 9SS, UK
R4 Astrophysics Research Institute, Liverpool John Moores University, Liverpool CH41 1LD, UK
R5 Max Planck Institute for Solar System Research, Max-Planck-Str. 2, 37191 Katlenburg-Lindau, Germany
R6 Qatar Environment and Energy Research Institute, Qatar Foundation, Tornado Tower, Floor 19, P.O. Box 5825, Doha, Qatar
N1 Niels Bohr Institute, Astronomical Observatory, Juliane Maries vej 30, 2100 Copenhagen, Denmark
N2 Qatar Foundation, P.O. Box 5825, Doha, Qatar
N3 Dipartimento di Fisica “E. R. Caianiello”, Università di Salerno, Via Giovanni Paolo II n. 132, 84084 Fisciano (SA), Italy
N4 International Institute for Advanced Scientific Studies (IIASS), 84019 Vietri sul Mare, (SA), Italy
N5 Centre for Star and Planet formation, Geological Museum, Øster Voldgade 5, 1350, Copenhagen, Denmark
N6 Dept. of Physics, Sharif University of Technology, P.O. Box 11155-9161, Tehran, Iran
N7 Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK
N8 Institut d’Astrophysique et de Géophysique, Allée du 6 Août 17, Sart Tilman, Bât. B5c, 4000 Liége, Belgium
N9 Boston University, Astronomy Department, 725 Commonwealth Avenue, Boston, MA 02215, USA
N10 Armagh Observatory, College Hill, Armagh, BT61 9DG, Northern Ireland, UK
N11 Korea Astronomy and Space Science Institute, 776 Daedukdae-ro, Yuseong-gu, Daejeon 305-348, Korea
N12 Jodrell Bank Centre for Astrophysics, University of Manchester, Oxford Road,Manchester, M13 9PL, UK
N13 Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany
N14 Instituto de Astrofísica, Facultad de Física, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, 7820436 Macul, Santiago, Chile
N15 Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität Heidelberg (ZAH), Mönchhofstr. 12-14, 69120 Heidelberg, Germany
N16 INFN, Gruppo Collegato di Salerno, Sezione di Napoli, Italy
N17 Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany
N18 Istituto Internazionale per gli Alti Studi Scientifici (IIASS),84019 Vietri Sul Mare (SA), Italy
N19 Main Astronomical Observatory, Academy of Sciences of Ukraine, vul. Akademika Zabolotnoho 27, 03680 Kyiv, Ukraine
O1 Warsaw University Observatory, Al. Ujazdowskie 4, 00-478 Warszawa, Poland
O2 Universidad de Concepción, Departamento de Astronomia, Casilla 160-C, Concepción, Chile
O3 Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
P1 University of Canterbury, Dept. of Physics and Astronomy, Private Bag 4800, 8020 Christchurch, New Zealand
P2 Université de Toulouse, UPS-OMP, IRAP, 31400 Toulouse, France
P3 CNRS, IRAP, 14 avenue Edouard Belin, 31400 Toulouse, France
P4 UPMC-CNRS, UMR7095, Institut d’Astrophysique de Paris, 98bis boulevard Arago, 75014 Paris, France
P5 European Southern Observatory (ESO), Alonso de Cordova 3107, Casilla 19001, Santiago 19, Chile
P6 McDonald Observatory, 16120 St Hwy Spur 78 #2, Fort Davis, TX 79734, USA
P7 School of Math and Physics, University of Tasmania, Private Bag 37, GPO Hobart, 7001 Tasmania, Australia
2
A REFINED ANALYSIS OF MICROLENSING EVENT OGLE-2012-BLG-0406
P8 Physics
Department, Faculty of Arts and Sciences, University of Rijeka, Omladinska 14, 51000 Rijeka, Croatia
University of Vienna, Department of Computing, Wiedner Hauptstrasse 10, Vienna, Austria
P10 Department of Physics & Astronomy, San Francisco State University, 1600 Holloway Avenue, San Francisco, CA 94132, USA
P11 Laboratory for Exoplanets and Stellar Astrophysics, Mail Code 667, NASA/GSFC, Bldg 34, Room E317, Greenbelt, MD 20771
P12 South African Astronomical Observatory, PO Box 9, Observatory 7935, South Africa
U 1 Department of Astronomy, Ohio State University, 140 West 18th Avenue, Columbus, OH 43210, USA
U 2 Department of Physics and Astronomy, Texas A&M University, College Station, TX 77843, USA
U 3 Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA
U 4 Korea Astronomy and Space Science Institute, Daejeon 305-348, Republic of Korea
U 5 Klein Karoo Observatory, Calitzdorp, and Bronberg Observatory, Pretoria, South Africa
U 6 Auckland Observatory, Auckland, New Zealand
U 7 Turitea Observatory, Palmerston North, New Zealand
U 8 Perth Exoplanet Survey Telescope, Perth, Australia
U 9 Possum Observatory, Patutahi, Gisbourne, New Zealand
U 10 School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv 69978, Israel
M1 Department of Earth and Space Science, Osaka University, Osaka 560-0043, Japan
M2 Solar-Terrestrial Environment Laboratory, Nagoya University, Nagoya, 464-8601, Japan
M3 Institute of Information and Mathematical Sciences, Massey University, Private Bag 102-904, North Shore Mail Centre, Auckland, New Zealand
M4 Department of Physics, University of Auckland, Private Bag 92-019, Auckland 1001, New Zealand
M5 School of Chemical and Physical Sciences, Victoria University, Wellington, New Zealand
M6 Okayama Astrophysical Observatory, National Astronomical Observatory of Japan, Asakuchi, Okayama 719-0232, Japan
M7 Nagano National College of Technology, Nagano 381-8550, Japan
M8 Tokyo Metropolitan College of Aeronautics, Tokyo 116-8523, Japan
M9 Mt. John University Observatory, P.O. Box 56, Lake Tekapo 8770, New Zealand
M10 University of Notre Dame, Department of Physics, 225 Nieuwland Science Hall, Notre Dame, IN 46556-5670, USA
M11 Department of Physics, Faculty of Science, Kyoto Sangyo University, 603-8555, Kyoto, Japan
♠ The RoboNet Collaboration
♦ The MiNDSTEp Collaboration
The OGLE Collaboration
‡ The µFUN Collaboration
♣ The PLANET Collaboration
† The MOA Collaboration
and
⋆ Corresponding author
Draft version October 10, 2013
P9 Technical
ABSTRACT
We present a detailed analysis of survey and follow-up observations of microlensing event OGLE-2012-BLG0406 based on data obtained from 10 different observatories. Intensive coverage of the lightcurve, especially
the perturbation part, allowed us to accurately measure the parallax effect and lens orbital motion. Combining
our measurement of the lens parallax with the angular Einstein radius determined from finite-source effects,
we estimate the physical parameters of the lens system. We find that the event was caused by a 2.73 ± 0.43 MJ
planet orbiting a 0.44 ± 0.07 M⊙ early M-type star. The distance to the lens is 4.97 ± 0.29 kpc and the projected
separation between the host star and its planet at the time of the event is 3.45 ± 0.26 AU. We find that the
additional coverage provided by follow-up observations, especially during the planetary perturbation, leads to
a more accurate determination of the physical parameters of the lens.
Subject headings: gravitational lensing – binaries: general – planetary systems
1. INTRODUCTION
Radial velocity and transit surveys, which primarily target
main-sequence stars, have already discovered hundreds of giant planets and are now beginning to explore the reservoir of
lower mass planets with orbit sizes extending to a few astronomical units (AU). These planets mostly lie well inside
the snow line1 of their host stars. Meanwhile, direct imaging with large aperture telescopes has been discovering giant planets tens to hundreds of AUs away from their stars.
The region of sensitivity of microlensing lies somewhere in
between and extends to low-mass exoplanets lying beyond
the snow-line of their low-mass host stars, between ∼1 and
10 AU (Tsapras et al. 2003; Gaudi 2012). Although there
is already strong evidence that cold sub-Jovian planets are
more common than originally thought around low-mass stars
∗ Royal
Society University Research Fellow
The snow line is defined as the distance from the star in a protoplanetary
disk where ice grains can form.
1
(Gould et al. 2006; Sumi et al. 2010; Kains et al. 2013), cold
super-Jupiters orbiting K or M-dwarfs were believed to be
a rarer class of objects2 (Laughlin et al. 2004; Cassan et al.
2012).
The theoretical framework that underpins planetary formation scenarios that could potentially result in such systems involves parameters that are currently too loosely constrained.
These parameters can be refined by tracing the distributions
of physical and orbital properties of a significant number of
planetary systems. The radial velocity method has been remarkably successful in tabulating the part of the distribution
that lies within the snow-line but discoveries of super-Jupiters
beyond the snow-line of M-dwarfs have been comparatively
few (Johnson et al. 2010; Montet et al. 2013). By contrast,
this is exactly the type of planet that microlensing is most
sensitive to (Gaudi 2012).
2 although a metal-rich protoplanetary disk might allow the formation of
sufficiently massive solid cores.
TSAPRAS ET AL.
Three brown dwarf and nineteen planet microlensing discoveries have been published to date, including the discoveries of two multiple-planet systems (Gaudi et al. 2008;
Han et al. 2013)3 . It is also worth noting that unbound objects
of planetary mass have also been reported (Sumi et al. 2011).
Microlensing involves the chance alignment along an observer’s line of sight of a foreground object (lens) and a background star (source). This results in a characteristic variation
of the brightness of the background source as it is being gravitationally lensed. As seen from the Earth, the brightness of
the source increases as it approaches the lens, reaching a maximum value at the time of closest approach. The brightness
then decreases again as the source moves away from the lens.
In microlensing events, planets orbiting the lens star can
reveal their presence through distortions in the otherwise
smoothly varying standard single lens lightcurve. Together,
the host star and planet constitute a binary lens. Binary lenses
have a magnification pattern that is more complex than the
single lens case due to the presence of extended caustics that
represent the positions on the source plane at which the lensing magnification diverges. Distortions in the lightcurve arise
when the trajectory of the source star approaches (or crosses)
the caustics (Mao and Paczyński 1991).
Upgrades to the OGLE4 (Udalski 2003) survey observing
setup and MOA5 (Sumi et al. 2003) microlensing survey telescope in the past couple of years brought greater precision
and enhanced observing cadence, resulting in an increased
rate of exoplanet discoveries. For example, OGLE has regularly been monitoring the field of the OGLE-2012-BLG0406 event since March 2010 with a cadence of 55 minutes.
When a microlensing alert was issued notifying the astronomical community that event OGLE-2012-BLG-0406 was
exhibiting anomalous behavior, intense follow-up observations from multiple observatories around the world were initiated in order to better characterize the deviation. This event
was first analyzed by Poleski et al. (2013) using exclusively
the OGLE-IV survey photometry. That study concluded that
the event was caused by a planetary system consisting of a
3.9±1.2 MJ planet orbiting a low mass late K/early M dwarf.
In this paper we present the analysis of the event based
on the combined data obtained from 10 different telescopes,
spread out in longitude, providing dense and continuous coverage of the lightcurve.
The paper is structured as follows: Details of the discovery of this event, follow-up observations and image analysis
procedures are described in Section 2. Section 3 presents the
methodology of modeling the features of the lightcurve. We
provide a summary and conclude in Section 4.
2. OBSERVATIONS AND DATA
Microlensing event OGLE-2012-BLG-0406 was discovered at equatorial coordinates α = 17h 53m 18.17s, δ =
−30◦ 28′ 16.2′′ (J2000.0)6 by the OGLE-IV survey and announced by their Early Warning System (EWS)7 on the 6th
of April 2012. The event had a baseline I-band magnitude of
16.35 and was gradually increasing in brightness. The predicted maximum magnification at the time of announcement
was low, therefore the event was considered a low-priority
3 For a complete list consult http://exoplanet.eu/catalog/ and references
therein.
4 http://ogle.astrouw.edu.pl
5 http://www.phys.canterbury.ac.nz/moa
6 (l, b) = −0.46◦ , −2.22◦
7 http://ogle.astrouw.edu.pl/ogle4/ews/ews.html
3
target for most follow-up teams who preferentially observe
high-magnification events as they are associated with a higher
probability of detecting planets (Griest and Safizadeh 1998).
OGLE observations of the event were carried out with the
1.3-m Warsaw telescope at the Las Campanas Observatory,
Chile, equipped with the 32 chip mosaic camera. The event’s
field was visited every 55 minutes providing very dense and
precise coverage of the entire light curve from the baseline,
back to the baseline. For more details on the OGLE data and
coverage see Poleski et al. (2013).
An assessment of data acquired by the OGLE team until the 1st of July (08:47 UT, HJD∼2456109.87) which
was carried out by the SIGNALMEN anomaly detector
(Dominik et al. 2007) on the 2nd of July (02:19 UT) concluded that a microlensing anomaly, i.e. a deviation from
the standard bell-shaped Paczyński curve (Paczyński 1986),
was in progress. This was electronically communicated
via the ARTEMiS (Automated Robotic Terrestrial Exoplanet
Microlensing Search) system (Dominik et al. 2008) to trigger prompt observations by both the RoboNet-II8 collaboration (Tsapras et al. 2009) and the MiNDSTEp9 consortium
(Dominik 2010). RoboNet’s web-PLOP system (Horne et al.
2009) reacted to the trigger by scheduling observations already from the 2nd of July (02:30 UT), just 11 minutes after the SIGNALMEN assessment started. However, the first
RoboNet observations did not occur before the 4th of July
(15:26 UT), when the event was observed with the FTS. This
delayed response was due to the telescopes being offline for
engineering work and bad weather at the observing sites. It
fell to the Danish 1.54m at ESO La Silla to provide the first
data point following the anomaly alert (2nd of July, 03:42 UT)
as part of the MiNDSTEp efforts. The alert also triggered automated anomaly modeling by RTModel (Bozza 2010), which
by the 2nd of July (04:22 UT) delivered a rather broad variety
of solutions in the stellar binary or planetary range, reflecting
the fact that the true nature was not well-constrained by the
data available at that time. This process chain did not involve
any human interaction at all.
The first human involvement was an e-mail circulated to all
microlensing teams by V. Bozza on the 2nd of July (07:26 UT)
informing the community about the ongoing anomaly and
modeling results. Including OGLE data from a subsequent
night, the apparent anomaly was also independently spotted
by E. Bachelet (e-mail by D.P. Bennett of 3rd July, 13:42 UT),
and subsequently PLANET10 team (Beaulieu et al. 2006)
SAAO data as well as µFUN11 (Gould et al. 2006) SMARTS
(CTIO) data were acquired the coming night, which along
with the RoboNet FTS data cover the main peak of the
anomaly. It should be noted that the observers at CTIO decided to follow the event even while the moon was full in
order to obtain crucial data. A model circulated by T. Sumi
on the 5th of July (00:38 UT) did not distinguish between the
various solutions.
However, when the rapidly changing features of the
anomaly were independently assessed by the Chungbuk National University group (CBNU, C. Han), the community was
informed on the 5th of July (10:43 UT) that the anomaly is
very likely due to the presence of a planetary companion.
An independent modeling run by V. Bozza’s automatic soft8
http://robonet.lcogt.net
http://www.mindstep-science.org
10 http://planet.iap.fr
11 http://www.astronomy.ohio-state.edu/∼microfun
9
4
A REFINED ANALYSIS OF MICROLENSING EVENT OGLE-2012-BLG-0406
TABLE 1. O BSERVATIONS
group
telescope
OGLE
RoboNet
RoboNet
RoboNet
MiNDSTEp
MOA
µFUN
PLANET
PLANET
WISE
1.3m Warsaw Telescope, Las Campanas Observatory (LCO), Chile
2.0m Faulkes North Telescope (FTN), Haleakala, Hawaii, USA
2.0m Faulkes South Telescope (FTS), Siding Spring Observatory (SSO), Australia
2.0m Liverpool Telescope (LT), La Palma, Spain
1.5m Danish Telescope, La Silla, Chile
0.6m Boller & Chivens (B&C), Mt. John, New Zealand
1.3m SMARTS, Cerro Tololo Inter-American Observatory (CTIO), Chile
1.0m Elizabeth Telescope, South African Astronomical Observatory (SAAO), South Africa
1.0m Canopus Telescope, Mt. Canopus Observatory, Tasmania, Australia
1.0m Wise Telescope, Wise Observatory, Israel
ware (5th of July, 10:55 UT) confirmed the result. While the
OGLE collaboration (A. Udalski) notified observers on the 5th
of July that a caustic exit was occurring, a geometry leading
to a further small peak successively emerged from the models. D.P. Bennett circulated a model using updated data on
the 6th of July (00:14 UT) which highlighted the presence of
a second prominent feature expected to occur ∼10th of July.
Another modeling run performed at CBNU on the 7th of July
(02:39 UT) also identified this feature and estimated that the
secondary peak would occur on the 11th of July.
Follow-up teams continued to monitor the progress of the
event intensively until the beginning of September, well after
the planetary deviation had ceased, and provided dense coverage of the main peak of the event. A preliminary model
using available OGLE and follow-up data at the time, circulated on the 31st of October (C. Han, J.-Y. Choi), classified the
companion to the lens as a super-Jupiter. Poleski et al. (2013)
presented an analysis of this event using reprocessed survey
data exclusively. In this paper we present a refined analysis
using survey and follow-up data together.
The groups that contributed to the observations of this
event, along with the telescopes used, are listed in Table 1.
Most observations were obtained in the I-band and some images were also taken in other bands in order to create a colormagnitude diagram and classify the source star. We note
that there are also observations obtained from the MOA 1.8m
survey telescope which we did not include in our modeling
because the target was very close to the edge of the CCD.
We also do not include data from the µFUN Auckland 0.4m,
PEST 0.3m, Possum 0.36m and Turitea 0.36m telescopes due
to poor observing conditions at site.
Extracting accurate photometry from observations of
crowded fields, such as the Galactic Bulge, is a challenging
process. Each image contains thousands of stars whose stellar
point-spread functions (PSFs) often overlap so aperture and
PSF-fitting photometry can at best offer limited precision. In
order to optimize the photometry it is necessary to use difference imaging (DI) techniques (Alard and Lupton 1998). For
any particular telescope/camera combination, DI uses a reference image of the event taken under optimal seeing conditions
which is then degraded to match the seeing conditions of every other image of the event taken from that telescope. The
degraded reference image is then subtracted from the matching image to produce a residual (or difference) image. Stars
that have not varied in brightness in the time interval between
the two images will cancel, leaving no systematic residuals
on the difference image but variable stars will leave either a
positive or negative residual.
DI is the preferred method of photometric analysis among
passband
I
I
I
I
I
I
V, I
I
I
I
data points
3013
83
121
131
473
1856
16, 81
226
210
180
microlensing groups and each group has developed custom
pipelines to reduce their observations. OGLE and MOA images were reduced using the pipelines described in Udalski
(2003) and Bond et al. (2001) respectively. PLANET, µFUN,
and WISE images were processed using variants of the PySIS
(Albrow et al. 2009) pipeline, whereas RoboNet and MiNDSTEp observations were analyzed using customized versions
of the DanDIA package (Bramich 2008). Once the source star
returned to its baseline magnitude, each data set was reprocessed to optimize photometric precision. These photometrically optimized data sets were used as input for our modeling
run.
3. MODELING
Figure 1 shows the lightcurve of OGLE-2012-BLG-406.
The lightcurve displays two main features that deviate significantly from the standard Paczyński curve. The first feature,
which peaked at HJD ∼ 2456112 (3rd of July), is produced
by the source trajectory grazing the cusp of a caustic. The
brightness then quickly drops as the source moves away from
the cusp, increases again for a brief period as it passes close to
another cusp at HJD ∼ 2456121 (12th of July), and eventually
returns to the standard shape as the source moves further away
from the caustic structure. The anomalous behavior, when
both features are considered, lasts for a total of ∼ 15 days,
while the full duration of the event is &120 days. These are
typical lightcurve features expected from lensing phenomena
involving planetary lenses.
We begin our analysis by exploring a standard set of solutions that involve modeling the event as a static binary lens.
The Paczyński curve representing the evolution of the event
for most of its duration is described by three parameters: the
time of closest approach between the projected position of the
source on the lens plane and the position of the lens photocenter12 , t0 , the minimum impact parameter of the source, u0 ,
expressed in units of the angular Einstein radius of the lens
(θE ), and the duration of time, tE (the Einstein time-scale), required for the source to cross θE . The binary nature of the lens
requires the introduction of three extra parameters: The mass
ratio q between the two components of the lens, their projected separation s, expressed in units of θE , and the source
trajectory angle α with respect to the axis defined by the two
12 The "photocenter" refers to the center of the lensing magnification pattern. For a binary-lens with a projected separation between the lens components less than the Einstein radius of the lens, the photocenter corresponds
to the center of mass. For a lens with a separation greater than the Einstein
radius, there exist two photocenters each of which is located close to each
lens component with an offset q/[s(1 + q)] toward the other lens component
(Kim et al. 2009). In this case, the reference t0 , u0 measurement is obtained
from the photocenter to which the source trajectory approaches closest.
TSAPRAS ET AL.
5
F IG . 1.— Lightcurve of OGLE-2012-BLG-0406 showing our best-fit binary-lens model including parallax and orbital motion. The legend on the right of the
figure lists the contributing telescopes. All data were taken in the I-band, except where otherwise indicated.
TABLE 2. L ENSING PARAMETERS
parameters
χ2 /dof
t0 (HJD’)
u0
tE (days)
s
q (10−3 )
α
ρ∗ (10−2 )
πE,N
πE,E
ds/dt (yr−1 )
dα/dt (yr−1 )
standard
6921.019/6383
6141.63 ± 0.04
0.532 ± 0.001
62.37 ± 0.06
1.346 ± 0.001
5.33 ± 0.04
0.852 ± 0.001
1.103 ± 0.008
–
–
–
–
parallax
orbit
u0 > 0
u0 < 0
u0 > 0
u0 < 0
6850.358/6381
6141.70 ± 0.05
0.527 ± 0.001
63.75 ± 0.18
1.345 ± 0.001
5.07 ± 0.03
0.864 ± 0.002
1.053 ± 0.007
0.118 ± 0.011
-0.033 ± 0.007
–
–
6677.685/6381
6141.66 ± 0.05
-0.520 ± 0.001
69.39 ± 0.32
1.341 ± 0.001
4.45 ± 0.04
-0.906 ± 0.002
0.968 ± 0.009
-0.414 ± 0.016
-0.069 ± 0.009
–
–
6408.371/6381
6141.24 ± 0.05
0.500 ± 0.002
65.33 ± 0.20
1.300 ± 0.002
6.97 ± 0.27
0.861 ± 0.002
1.233 ± 0.031
–
–
0.765 ± 0.046
1.284 ± 0.159
6408.255/6381
6141.28 ± 0.04
-0.499 ± 0.002
65.53 ± 0.15
1.301 ± 0.001
6.63 ± 0.05
-0.859 ± 0.001
1.194 ± 0.011
–
–
0.727 ± 0.017
-1.108 ± 0.019
orbit+parallax
u0 > 0
u0 < 0
6357.680/6379
6141.33 ± 0.05
0.496 ± 0.002
64.77 ± 0.19
1.301 ± 0.002
5.92 ± 0.11
0.837 ± 0.002
1.111 ± 0.014
-0.143 ± 0.018
0.047 ± 0.007
0.669 ± 0.028
0.497 ± 0.059
6381.358/6379
6141.19 ± 0.06
-0.497 ± 0.002
61.91 ± 0.42
1.296 ± 0.002
6.82 ± 0.19
-0.810 ± 0.005
1.207 ± 0.023
0.358 ± 0.042
0.008 ± 0.006
0.802 ± 0.033
-0.732 ± 0.085
N OTE. — HJD’=HJD-2450000.
components of the lens. A seventh parameter, ρ∗ , representing
the source radius normalized by the angular Einstein radius
is also required to account for finite-source effects that are
important when the source trajectory approaches or crosses a
caustic.
The magnification pattern produced by binary lenses is very
sensitive to variations in s, q, which are the parameters that
affect the shape and orientation of the caustics, and α, the
source trajectory angle. Even small changes in these parameters can produce extreme changes in magnification as they
may result in the trajectory of the source approaching or crossing a caustic. On the other hand, changes in the other parameters cause the overall magnification pattern to vary smoothly.
To assess how the magnification pattern depends on the parameters, we start the modeling run by performing a hybrid
search in parameter space whereby we explore a grid of s, q, α
values and optimize t0 , u0 ,tE and ρ∗ at each grid point by
χ2 minimization using Markov Chain Monte Carlo (MCMC).
Our grid limits are set at −1 ≤ log s ≤ 1, −5 ≤ log q ≤ 1, and
0 ≤ α < 2π, which are wide enough to guarantee that all local
minima in parameter space have been identified. An initial
MCMC run provides a map of the topology of the χ2 surface,
which is subsequently further refined by gradually narrowing down the grid parameter search space (Shin et al. 2012a;
Street et al. 2013). Once we know the approximate locations
of the local minima, we perform a χ2 optimization using all
6
A REFINED ANALYSIS OF MICROLENSING EVENT OGLE-2012-BLG-0406
seven parameters at each of those locations in order to determine the refined position of the minimum. From this set of
local minima, we identify the location of the global minimum
and check for the possible existence of degenerate solutions.
We find no other solutions.
F IG . 2.— The bottom panel zooms-in on the anomalous region of the
lightcurve presented in Figure 1. At the top panel we display the source trajectory, color coded for the individual contributions of each observatory, and
caustic structure at two different times corresponding to the first and second peaks of the anomaly. All scales are normalized by θE , and the size of
the circles corresponds to the size of the source. The first peak deviates the
strongest. This is a result of the trajectory of the source grazing the cusp of
the caustic at t1 (HJD∼2456112), shown in red. The second deviation at t2
(HJD∼2456121) is significantly weaker and is due to the source trajectory
passing close to another cusp of the caustic, shown in blue. The differences
in the shape of the caustic shown at t1 and t2 are due to the orbital motion of
the lens-planet system.
Since our analysis relies on data sets obtained from different telescopes and instruments which use different estimates for the reported photometric precision, we normalize
the flux uncertainties of each data set by adjusting them as
ei = fi (σ02 + σi2 )1/2 , where fi is a scale factor, σ0 are the originally reported uncertainties and σi is an additive uncertainty
term for each data set i. The rescaling ensures that χ2 per degree of freedom (χ2 /dof) for each data set relative to the model
becomes unity. Data points with very large uncertainties and
obvious outliers are also removed in the process.
In computing finite-source magnifications, we take into account the limb-darkening of the source by modeling the surface brightness as Sλ (ϑ) ∝ 1 − Γλ (1 − 1.5 cosϑ) (Albrow et al.
2001), where ϑ is the angle between the line of sight toward
the source star and the normal to the source surface, and Γλ
is the limb-darkening coefficient in passband λ. We adopt
ΓV = 0.74 and ΓI = 0.53 from the Claret (2000) tables. These
values are based on our classification of the stellar type of the
source, as subsequently described.
The residuals contained additional smooth structure that the
static binary model did not account for. This indicated the
need to consider additional second-order effects. The event
lasted for & 120 days, so the positional change of the observer
caused by the orbital motion of the Earth around the Sun may
have affected the lensing magnification. This introduces subtle long-term perturbations in the event lightcurve by causing
the apparent lens-source motion to deviate from a rectilinear
trajectory (Gould 1992; Alcock et al. 1995). Modeling this
parallax effect requires the introduction of two extra parameters, πE,N and πE,E , representing the components of the parallax vector π E projected on the sky along the north and east
equatorial axes respectively (Gould et al. 2004).
An additional effect that needs to be considered is the orbital motion of the lens system. The lens orbital motion
causes the shape of the caustics to vary with time. To a first order approximation, the orbital effect can be modeled by introducing two extra parameters that represent the rate of change
of the normalized separation between the two lensing components ds/dt and the rate of change of the source trajectory
angle relative to the caustics dα/dt (Albrow et al. 2000).
We conduct further modeling considering each of the
higher-order effects separately and also model their combined
effect. Furthermore, for each run considering a higher-order
effect, we test models with u0 > 0 and u0 < 0 that form a pair
of degenerate solutions resulting from the mirror-image symmetry of the source trajectory with respect to the binary-lens
axis. For each model, we repeat our calculations starting from
different initial positions in parameter space to verify that the
fits converge to our previous solution and that there are no
other possible minima.
Table 2 lists the optimized parameters for the models we
considered. We find that higher-order effects contribute
strongly to the shape of the lightcurve. The model including the parallax effect provides a better fit than the standard
model by ∆χ2 = 243.3. The orbital effect also improves the
fit by ∆χ2 = 512.8. The combination of both parallax and
orbital effects improves the fit by ∆χ2 = 563.3. Due to the
u0 > 0 and u0 < 0 degeneracy, there are two solutions for the
orbital motion + parallax model which have similar χ2 values.
In Figure 1, we present the best-fit model lightcurve superposed on the observed data. Figure 2 displays an enlarged
view of the perturbation region of the lightcurve along with
the source trajectory with respect to the caustic. The followup observations cover critical features of the perturbation regions that were not covered by the survey data. We note that
the caustic varies with time and thus we present the shape of
the caustic at the times of the first (t1 =HJD∼2456112) and
second perturbations (t2 =HJD∼2456121). The source trajectory grazes the caustic structure at t1 causing a substantial increase in magnification. As the caustic structure and trajectory evolve with time, the trajectory approaches another cusp
at t2 , but does not cross it. This second approach causes an increase in magnification which is appreciably lower than that
of the first encounter at t1 . The source trajectory is curved due
to the combination of the parallax and orbital effects.
The mass and distance to the lens are determined by
AU
θE
;
DL =
,
(1)
Mtot =
κπE
πE θE + πS
where κ = 4G/(c2 AU) and πS is the parallax of the source
star (Gould 1992). To determine these physical quantities we
require the values of πE and θE . Modeling the event returns
TSAPRAS ET AL.
the value of πE , whereas θE = θ∗ /ρ∗ depends on the angular
radius of the source star, θ∗ , and the normalized source radius, ρ∗ , which is also returned from modeling (see Table 2).
Therefore, determining θE requires an estimate of θ∗ .
To estimate the angular source radius, we use the standard method described in Yoo et al. (2004). In this procedure we first measure the dereddened color and brightness
of the source star by using the centroid of the giant clump
as a reference because its dereddened magnitude I0,c = 14.45
(Nataf et al. 2013) and color (V − I)0,c = 1.06 (Bensby et al.
2011) are already known. For this calibration, we use a colormagnitude diagram obtained from CTIO observations in the
I and V bands. We then convert the V − I source color to
V − K using the color-color relations from Bessell and Brett
(1988) and the source radius is obtained from the θ∗ -(V − K)
relations of Kervella et al. (2004). We derive the dereddened
magnitude and color of the source star as I0 = 14.62 and
(V − I)0 = 1.12 respectively. This confirms that the source star
is an early K-type giant. The estimated angular source radius
is θ∗ = 5.94 ± 0.51 µas. Combining this with our evaluation
of ρ∗ , we obtain θE = 0.53 ± 0.05 mas for the angular Einstein
radius of the lens.
F IG . 3.— ∆χ2 contours for the parallax parameters derived from our
MCMC fits for the best binary-lens model including orbital motion and the
parallax effect.
Our analysis is consistent with the results of Poleski et al.
(2013). We confirm that the lens is a planetary system composed of a giant planet orbiting a low-mass star and we report
the refined parameters of the system. Poleski et al. (2013) reported that there existed a pair of degenerate solutions with
u0 > 0 and u0 < 0, although the positive u0 solution is slightly
preferred with ∆χ2 = 13.6. We find a consistent result that
the positive u0 solution is preferred but the degeneracy is better discriminated by ∆χ2 = 23.7.
The error contours of the parallax parameters for the best-fit
model are presented in Figure 3. The uncertainty of each parameter is determined from the distribution of MCMC chain,
and the reported uncertainty corresponds to the standard devi-
7
TABLE 3. P HYSICAL PARAMETERS
parameters
quantity
Mass of the host star (M⋆ )
Mass of the planet (Mp )
Distance to the lens (DL )
Projected star-planet separation (d⊥ )
Einstein radius (θE )
Geocentric proper motion (µGeo )
0.44 ± 0.07 M⊙
2.73 ± 0.43 MJ
4.97 ± 0.29 kpc
3.45 ± 0.26 AU
0.53 ± 0.05 milli-arcsec
3.02 ± 0.26 milli-arcsec yr−1
ation of the distribution. We list the physical parameters of the
system in Table 3 and their posterior probability distributions
are shown in Figure 4.
The lens lies DL = 4.97 ± 0.29 kpc away in the direction
of the Galactic Bulge. The more massive component of the
lens has mass M⋆ = 0.44 ± 0.07 M⊙ so it is an early M-type
dwarf star and its companion is a super-Jupiter planet with a
mass Mp = 2.73 ± 0.43 MJ . The projected separation between
the two components of the lens is d⊥ = 3.45 ± 0.26 AU. The
geocentric relative proper motion between the lens and the
source is µGeo = θE /tE = 3.02 ± 0.26 milli-arcsec yr−1 . In the
Heliocentric frame, the proper motion is µHelio = (µN , µE ) =
(−2.91 ± 0.26, 1.31 ± 0.16) milli-arcsec yr−1 .
We note that the derived physical lens parameters are somewhat different from those of Poleski et al. (2013). Specifically, the mass of the lens system derived in Poleski et al.
(2013) is 0.59 M⊙ , which is ∼ 34% greater than our estimate.
Half of this difference comes from the slightly larger Einstein
radius obtained by Poleski et al. (2013) from the OGLE-IV
photometry and the remaining part from the slightly larger
πE,N component of the parallax obtained from modeling the
survey and follow-up photometry as presented in this paper.
It should be noted that the parameters derived by both our and
thePoleski et al. (2013) models are consistent within the 1-σ
level.
To further check the consistency between our model and
that of Poleski et al. (2013), we conducted additional modeling based on different combinations of data sets. We first
test a model based on OGLE data exclusively in order to see
whether we can retrieve the physical parameters reported in
Poleski et al. (2013). From this modeling, we derive physical parameters consistent with those of Poleski et al. (2013),
indicating that the differences are due to the additional coverage provided by the follow-up observations. We conducted
another modeling run using OGLE observations but also included CTIO, FTS and SAAO data, i.e. those datasets covering the anomalous peak. This modeling run resulted in physical parameters that are consistent with the values extracted
from fitting all combined data together, as reported in this paper. This indicates that the differences between Poleski et al.
(2013) and this analysis, although consistent within the 1-σ
level, come mainly from follow-up data that provide better
coverage of the perturbation. Therefore, using survey and
follow-up data together, we arrive at a more accurate determination of the ρ and πE,N parameters, which leads to a refinement of the physical parameters of the planetary system.
4. CONCLUSIONS
Microlensing event OGLE-2012-BLG-0406 was intensively observed by survey and follow-up groups using 10 different telescopes around the world. Anomalous deviations observed in the lightcurve were recognized to be due to the pres-
8
A REFINED ANALYSIS OF MICROLENSING EVENT OGLE-2012-BLG-0406
F IG . 4.— The physical parameter uncertainties pertaining to the lens as derived from the MCMC runs optimizing our binary-lens model including parallax and
orbital motion for the u0 > 0 trajectory.
ence of a planetary companion even before the event reached
its central peak. The anomalous behavior was first identified
and assessed automatically via software agents. Most followup teams responded to these alerts by adjusting their observing strategies accordingly. This highlights the importance of
circulating early models to the astronomical community that
help to identify important targets for follow-up observations
(Shin et al. 2012b).
Our analysis of the combined data is consistent with the results of Poleski et al. (2013) and we report the refined parameters of the system. The primary lens with mass M⋆ = 0.44 ±
0.07 M⊙ is orbited by a planetary companion with mass Mp =
2.73 ± 0.43 MJ at a projected separation of d⊥ = 3.45 ± 0.26
AU. The distance to the system is DL = 4.97 ± 0.29 kpc in the
direction of the Galactic Bulge.
This is the fourth super-Jupiter planet around a lowmass star discovered by microlensing (Dong et al. 2009;
Batista et al. 2011; Yee et al. 2012) and the first such system
whose characteristics were derived solely from microlensing
data, without considering any external information.
The precise mechanism of how these objects form and
evolve around low mass stars is still an open question.
Simulations using the core accretion formalism can produce
such objects within reasonable disk lifetimes of a few Myr
(Mordasini et al. 2012) provided the core mass is sufficiently
large or the opacity of the planet envelope during gas
accretion is decreased by assuming that the dust grains have
grown to larger sizes than the typical interstellar values (R.
Nelson, private communication). Furthermore, gravitational
instability models of planet formation can also potentially
produce such objects when the opacity of the protoplanetary
disk is low enough to allow local fragmentation at greater
distances from the host star, and subsequently migrating the
planet to distances of a few AU.
YT thanks the CBNU group for their advice and hospitality while in Korea. DMB, MD, KH, CS, RAS, KAA,
MH and YT are supported by NPRP grant NPRP-09-4761-78 from the Qatar National Research Fund (a member of
Qatar Foundation). CS received funding from the European
Union Seventh Framework Programme (FP7/2007-2013) under grant agreement no. 268421. KH is supported by a
Royal Society Leverhulme Trust Senior Research Fellowship.
The OGLE project has received funding from the European
Research Council under the European Community’s Seventh
Framework Programme (FP7/2007-2013) / ERC grant agreement no. 246678 to AU. Work by CH was supported by
Creative Research Initiative Program (2009-0081561) of National Research Foundation of Korea. The MOA experiment
was supported by grants JSPS22403003 and JSPS23340064.
TS acknowledges the support JSPS24253004. TS is supported by the grant JSPS23340044. TCH acknowledges
support from KRCF via the KRCF Young Scientist Fellowship program and financial support from KASI grant number 2013-9-400-00. YM acknowledges support from JSPS
grants JSPS23540339 and JSPS19340058. AG and BSG acknowledge support from NSF AST-1103471. MR acknowledges support from FONDECYT postdoctoral fellowship
No3120097. BSG, AG, and RWP acknowledge support from
NASA grant NNX12AB99G. YD, AE and JS acknowledge
support from the Communaute francaise de Belgique - Actions de recherche concertees - Academie Wallonie-Europe.
This work is based in part on data collected by MiNDSTEp
with the Danish 1.54m telescope at the ESO La Silla Observatory. The Danish 1.54m telescope is operated based on a
grant from the Danish Natural Science Foundation (FNU).
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